scholarly journals Robustness of Majorana Zero-energy State in a Spin-orbit Coupled Semiconductor/superconductor Heterostructure

2021 ◽  
Author(s):  
Zheng Wang
Keyword(s):  
Differential Equation ◽  
Energy State ◽  
Numerical Test ◽  
Spin Orbit ◽  
Zero Energy ◽  
Topological Quantum ◽  
Linearized Stability ◽  
The Stability ◽  
Topological Quantum Computation ◽  
Coupled Semiconductor

Abstract Based on the principle of linearized stability proposed by Lyapounov, we investigate the robustness of Majorana zero energy state (MZES), which plays an important role in topological quantum computation. Our study is different from previous works that usually explore the stability of MZES by the numerical test of some special perturbations, our treatment is suitable for arbitrary perturbations. Since our method follows the stability theory of differential equation, the results we obtained are reliable. As an example, we demonstrate it by the stability of MZES in the spin-orbit coupled semiconductor/ superconductor junction, the analytical and numerical results indicate that the MZES is unstable in this system.

scholarly journals The simulation of non-Abelian statistics of Majorana fermions in Ising chain with Z2 symmetry

2017 ◽  
Vol 31 (11) ◽  
pp. 1750123
Author(s):  
Xiao-Ming Zhao ◽  
Jing Yu ◽  
Jing He ◽  
Qiu-Bo Cheng ◽  
Ying Liang ◽  
...  
Keyword(s):  
Transverse Field ◽  
Spin Model ◽  
Majorana Fermions ◽  
Spin Representation ◽  
Ising Chain ◽  
Zero Energy ◽  
Topological Quantum ◽  
Transverse Field Ising Model ◽  
Topological Quantum Computation ◽  
Symmetry Protected

In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions at the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana representation and spin representation are presented. The degenerate ground states of a symmetry protected spin chain therefore provide a promising platform for topological quantum computation.

Fidelity susceptibility in multiband one-dimensional topological superconducting system

2015 ◽  
Vol 29 (25n26) ◽  
pp. 1542034
Author(s):  
Wen-Chuan Tian ◽  
Zhi Wang ◽  
Dao-Xin Yao
Keyword(s):  
Phase Transition ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Topological Properties ◽  
Zero Energy ◽  
One Dimensional ◽  
Pure System ◽  
Zeeman Field ◽  
Disorder Effects ◽  
Topological Quantum

We use the fidelity susceptibility to study the topological properties of multi-layer nanowire system, with intrinsic spin–orbit coupling and proximity induced superconductivity. We introduce a Hamiltonian of three layer lattice chain to model the system, and consider the effects of applied Zeeman field. In pure system, we find a peak in fidelity susceptibility, which signals the topological quantum phase transition (TQPT) in the system. We then study the disorder effects in our model and find more peaks in fidelity susceptibility. We reveal that these peaks provide information on the zero energy Majorana states of the system, which appear after the TQPT.

AN INDEX THEOREM FOR GRAPHENE

2007 ◽  
Vol 21 (30) ◽  
pp. 5113-5120 ◽  
Author(s):  
JIANNIS K. PACHOS ◽  
MICHAEL STONE
Keyword(s):  
Graphene Sheet ◽  
Good Description ◽  
Index Theorem ◽  
Continuous Limit ◽  
Zero Energy ◽  
Arbitrary Geometry ◽  
Numerical Studies ◽  
Topological Quantum ◽  
Potential Applications ◽  
Topological Quantum Computation

We consider a graphene sheet folded in an arbitrary geometry, compact or with nanotube-like open boundaries. In the continuous limit, the Hamiltonian takes the form of the Dirac operator, which provides a good description of the low energy spectrum of the lattice system. We derive an index theorem that relates the zero energy modes of the graphene sheet with the topology of the lattice. The result coincides with analytical and numerical studies for the known cases of fullerene molecules and carbon nanotubes, and it extends to more complicated molecules. Potential applications to topological quantum computation are discussed.

scholarly journals Experimental review on Majorana zero-modes in hybrid nanowires

2021 ◽  
Vol 64 (10) ◽  
Author(s):  
Ji-Bang Fu ◽  
Bin Li ◽  
Xin-Fang Zhang ◽  
Guang-Zheng Yu ◽  
Guang-Yao Huang ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Zero Mode ◽  
Fault Tolerant ◽  
Energy State ◽  
Majorana Fermion ◽  
Zero Energy ◽  
Semiconductor Nanowire ◽  
Topological Quantum ◽  
The Status ◽  
Hybrid Devices

AbstractAs the condensed matter analog of Majorana fermion, the Majorana zero-mode is well known as a building block of fault-tolerant topological quantum computing. This review focuses on the recent progress of Majorana experiments, especially experiments about semiconductor-superconductor hybrid devices. We first sketch Majorana zero-mode formation from a bottom-up view, which is more suitable for beginners and experimentalists. Then, we survey the status of zero-energy state signatures reported recently, from zero-energy conductance peaks, the oscillations, the quantization, and the interactions with extra degrees of freedom. We also give prospects of future experiments for advancing one-dimensional semiconductor nanowire-superconductor hybrid materials and devices.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Strong and tunable spin–orbit interaction in a single crystalline InSb nanosheet

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Yuanjie Chen ◽  
Shaoyun Huang ◽  
Dong Pan ◽  
Jianhong Xue ◽  
Li Zhang ◽  
...  
Keyword(s):  
Layer Structure ◽  
Orbit Interaction ◽  
Spin Orbit ◽  
Device Layer ◽  
Physical Origin ◽  
Quantum Devices ◽  
Spin Orbit Interaction ◽  
Topological Quantum ◽  
Narrow Bandgap ◽  
Dual Gate

AbstractA dual-gate InSb nanosheet field-effect device is realized and is used to investigate the physical origin and the controllability of the spin–orbit interaction in a narrow bandgap semiconductor InSb nanosheet. We demonstrate that by applying a voltage over the dual gate, efficiently tuning of the spin–orbit interaction in the InSb nanosheet can be achieved. We also find the presence of an intrinsic spin–orbit interaction in the InSb nanosheet at zero dual-gate voltage and identify its physical origin as a build-in asymmetry in the device layer structure. Having a strong and controllable spin–orbit interaction in an InSb nanosheet could simplify the design and realization of spintronic deceives, spin-based quantum devices, and topological quantum devices.

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